Copula Based Discretized Bayesian Networks
Open Access DepositedBayesian Networks are probabilistic inference models that use graphs to represent the independenceassumptions between random variables(nodes). Due to their graphical nature, they enjoy great appeal as explainable inference models and consequently, interest in them has spawned multiple software libraries. In all of these computer programs, probabilistic inference takes place by computing updated probabilities in light of evidence, with different types of algorithms applicable to discrete and continuous networks. Commonly used methodologies are subject to the curse of dimensionality, a computational constraint arising due to three factors: the number of variables, the number of possible states for each variable, and in the case of continuous networks, the discretization levels selected. In spite of the inherent computational complexity, there are successful applications of discrete networks with thousands of nodes; a feat that has proven more difficult for large continuous networks. In addition, while the underlying graph embodies the independence assumptions, typical Bayesian Networks methodologies do not provide the means to easily specify correlations between nodes as design parameters. In this work, a Bayesian Network parameterization methodology is proposed that enables the joint specification of prescribed dependence degrees and marginals combined with a discretization scheme that approximates a continuous network via a discretized counterpart. The continuous networks here modeled are based on copula models of dependence, i.e. joint distributions with uniform marginals that capture dependence between random variables that enable the choice of marginals for each node. The proposed discretization approach is based on numerical integration methods that yield discrete marginals matching the first 2n − 1 moments of the original continuous distribution, where n denotes the selected discretization level. The resulting discretized network not only approximates pre-specified degrees of correlation between nodes, but is also portable into any discrete network software. Finally, comprehensive numerical results are presented for Bayesian Networks with predefined architectures.
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Zavaleta_gwu_0075A_16793.pdf | 2024-10-02 | Open Access |
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